We present an analysis of Fast Auroral Snapshot perpendicular electric field observations using both ion distributions and electric field measurements in auroral downward current regions to study the full DC E$perp$ (electric field perpendicular to the geomagnetic field) and potential structures. We use the electric field data from the field instrument for the spin-plane component of E$perp$, and the ion drift measurements for the axial DC E$perp$. Examining 71 return current region crossings, a significant fraction (more than half) show E$perp$ signatures during strong field events indicative of curved potential structures rather than idealized straight arcs. We define sheetlike structured events as those for which the ratio of the two E$perp$ components remains constant during the spacecraft crossing, and curved structures as those where the ratio varies. Sheetlike structures can be interpreted as straight arcs, but curved structures require gradients in another dimension. A statistical comparison shows parametric differences between sheetlike and curved structures; however, the distinction between sheetlike and curved events cannot be sorted clearly using j$parallel$, E$perp$, or scale length. Using the full DC electric field vector, we can investigate the morphology of auroral return current potential structures and inconsistencies with idealized static return current models. In this paper we present the observed spatial structures; in a companion paper we explore the implications of these observations.